Prime p₀= 2623658258827777019 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 70 2 28 2 4 2 28 2 (?)
a_n: 0 2 30 32 60 62 132 134 162 164 168 170 198 200
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 200
Found by: JayPi
db: batch=82, k=14, 28 28 70 28 4 28

SPT(16)	2623656165045064613	0 18 38 44 120 144 164 170 204 210 230 254 330 336 356 374	-2093782712406
SPT(16)	2623656184416381859	0 10 12 30 40 42 78 120 142 184 220 222 232 250 252 262	-2074411395160
SPT(16)	2623656592733646121	0 12 42 60 70 72 108 130 150 172 208 210 220 238 268 280	-1666094130898
SPT(16)	2623656942062031653	0 18 26 74 86 138 150 200 204 254 266 318 330 378 386 404	-1316765745366
STPT(10)	2623657956747653897	0 2 30 32 42 44 54 56 84 86	-302080123122
TPT(14)	2623658032923447809	0 2 18 20 48 50 78 80 210 212 252 254 282 284	-225904329210
SPT(16)	2623658342039043511	0 70 102 118 156 198 208 222 256 270 280 322 360 376 408 478	83211266492
SPT(16)	2623658730653977487	0 56 60 66 74 144 170 186 230 246 272 342 350 356 360 416	471826200468
STPT(10)	2623658960168243867	0 2 72 74 102 104 132 134 204 206	701340466848
SPT(16)	2623659034188023917	0 4 12 30 40 46 54 82 114 142 150 156 166 184 192 196	775360246898
SPT(16)	2623659087361915777	0 16 84 102 124 126 150 172 234 256 280 282 304 322 390 406	828534138758